The Management of Market Risk
• In the previous chapters, we spent a large amount of
time describing how risks can be measured
• In this chapter, we discuss how risk measurement is
used in risk management
• A bank's risk-management function is typically headed
by the chief risk officer (CRO)
• Reporting to the CRO will be
– the chief credit officer
– the chief market risk officer
– the chief operating risk officer
• Within the market-risk organization there are three
– policies and procedures
– risk measurement
– risk management
Setting VaR Limits
• the VaR limits would be set by starting with the
total capital available to the trading operation
and relating that to the maximum amount of VaR
that can be supported by that capital
• For regulatory capital, the relationship is as
Setting VaR Limits
• This sets the VaR limit for the trading operation
as a whole
• For the portfolios within the trading operation,
the VaR limit (VaRL) should be set including the
average correlation between each portfolio
• If there were only two portfolios, this would be as
VaRL2All = VaRL21 + VaRL22 + 2 ρ1,2 VaRL1 VaRL2
Setting VaR Limits
• we know the limit for all trading (VaRLAll)
and we know the average correlation
between the two portfolios (ρ1,2 )
• We can therefore use the quadratic
equation to get VaRL2 in terms of VaRL1
Setting VaR Limits
• The optimal amount to be allocated to each portfolio
depends on the expected return per unit of stand-alone
• Consider an example in which one business unit is
expected to return $1.5 per dollar of VaR
• Another is expected to return $1.3 per dollar of VaR
• Let us assume that the correlation between them (ρ1,2 ) is
0.3, and that the VaR limit for the trading operation
(VaRLAll) is $100
• Table 11-1 shows different values for VaRL1 and the
consequent values for VaRL2 to ensure that the total VaR
remains at $100
• It also shows the expected revenue from each desk and
the total revenue
Setting VaR Limits
For this example,
the total revenue is
expected to be
maximized if VaRL1
equals $70 and
VaRL2 equals $53
Setting VaR Limits
• For strategic purposes, market-risk managers typically
set the VaR limits for the major desks and allow the
heads of the desks to set limits for the subordinate desks
• For subordinate desks, the limits may be translated from
VaR into a measure that is more familiar to the trader,
such as duration dollars or Greeks
• To translate from VaR to duration dollars we reverse the
process used to calculate VaR from duration:

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